Ross also surrendered two singles and two walks in the third as Cleveland extended its lead to 3-0.
In his fourth Cactus League outing, Indians starter Corey Kluber started out strong before ultimately giving up three runs on six hits in four innings. The Padres did not have a runner advance past second base until the fourth, when they tallied three doubles and a single to tie the game at 3.
"I might have gotten a little bit tired there in the fourth, being out there for a little while," Kluber said. "Legs might have gotten a little bit heavy, left a few balls up. Overall, I felt pretty good."
Cleveland broke the tie in the fourth when Nyjer Morgan scored on a wild pitch from Leonel Campos, but San Diego battled back on Xavier Nady's first homer of the spring.
Morgan was 2-for-5 with a single and a double.
The Indians' fifth run came in the bottom of the seventh, when Matt Carson hit a chopper to third base and Alex Castellanos' throw was off the bag, allowing Ryan Rohlinger to score.
Santana, battling for the Cleveland third base job, also made a nice leaping catch to rob Chris Denorfia of a hit and likely an RBI in the top of the third.
San Diego's Alex Dickerson had a double and his seventh RBI of the spring.
Up next: Outfielder Ryan Raburn said Wednesday he hopes to be back in the big league lineup after notching two hits in a "B" game Tuesday. After missing time with a left knee contusion, he would be lending a hand -- Raburn is 6-for-10 with two homers, two doubles, four RBIs and three runs -- to right-hander Zach McAllister, who will start against the Royals. The game will be broadcast on SportsTime Ohio and on an exclusive webcast at 4:05 p.m. CST.
Joey Nowak is a reporter for MLB.com. Follow him on Twitter at @joeynowak. This story was not subject to the approval of Major League Baseball or its clubs.